Visible crew/equipment: In the first scene of the Christmas party when Takagi steps out of one the offices and greets a couple of his guests, the camera pans left to show the orchestra and other guests. A huge shadow of the camera and its operator is being shown on the back wall, then the stage light gets moved to light a different area and the shadow is gone. (00:02:20)
Visible crew/equipment: When Al goes into the lobby of the building, he walks over to a large reflective marble counter. If you look at this counter you can very plainly see the reflection of a large metal stage lamp hanging right over the actors' heads. (00:52:25)
Visible crew/equipment: Everyone is surprised when Karl is alive at the end of the movie because he appeared to be dead when hanging by the chain that McClane had wrapped around his neck. However, if you look at the back of Karl's head during the entire scene, you can see the safety wire coming out of the back of his shirt that holds him up. No wonder he survived. (01:48:45)
Visible crew/equipment: When McClane is crawling under the long table to get closer to hear the terrorists' conversation, you can see the reflection of the camera operator's legs following along with him on the table base. (00:29:15)
Visible crew/equipment: Just after John has shot Hans, he falls and smashes the glass window. Look behind him: you can see a wire in two shots. It's meant to hold the stunt double for either Holly or Hans. No slow-mo required.
Visible crew/equipment: When one of the terrorists enters an abandoned floor, logically the floor should be empty, but you can see the casting crew in the reflection of the windows. (00:35:00)
Visible crew/equipment: In scene on the top floor after John hits the fire alarm, as he is seeing the fire trucks coming and then turns away, once the lights are turned on, you can see the reflection of a number of crew people in the window during/after the cut away. One dude in a green shirt, another in a white shirt are prominent. (00:41:00)
Visible crew/equipment: When the car and truck drive upto the building, the truck goes down a ramp - another moving shadow can be seen cast over the car, from the camera crew.